document.write( "Question 687136: 2w^2+13w+20 I need help I don't know how to factor this \n" ); document.write( "

Algebra.Com's Answer #425049 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2w%5E2%2B13w%2B20\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"13\"$ , and the last term is $\"20\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"20\"$ to get $\"%282%29%2820%29=40\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"40\"$ (the previous product) and add to the second coefficient $\"13\"$ ?\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"40\"$ (the previous product).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factors of $\"40\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,8,10,20,40\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-8,-10,-20,-40\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"40\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*40 = 40
\n" ); document.write( "2*20 = 40
\n" ); document.write( "4*10 = 40
\n" ); document.write( "5*8 = 40
\n" ); document.write( "(-1)*(-40) = 40
\n" ); document.write( "(-2)*(-20) = 40
\n" ); document.write( "(-4)*(-10) = 40
\n" ); document.write( "(-5)*(-8) = 40\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"13\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

First Number	Second Number	Sum
1	40	1+40=41
2	20	2+20=22
4	10	4+10=14
5	8	5+8=13
-1	-40	-1+(-40)=-41
-2	-20	-2+(-20)=-22
-4	-10	-4+(-10)=-14
-5	-8	-5+(-8)=-13

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"5\"$ and $\"8\"$ add to $\"13\"$ (the middle coefficient).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the two numbers $\"5\"$ and $\"8\"$ both multiply to $\"40\"$ and add to $\"13\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"13w\"$ with $\"5w%2B8w\"$ . Remember, $\"5\"$ and $\"8\"$ add to $\"13\"$ . So this shows us that $\"5w%2B8w=13w\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2w%5E2%2Bhighlight%285w%2B8w%29%2B20\"$ Replace the second term $\"13w\"$ with $\"5w%2B8w\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%282w%5E2%2B5w%29%2B%288w%2B20%29\"$ Group the terms into two pairs.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"w%282w%2B5%29%2B%288w%2B20%29\"$ Factor out the GCF $\"w\"$ from the first group.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"w%282w%2B5%29%2B4%282w%2B5%29\"$ Factor out $\"4\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28w%2B4%29%282w%2B5%29\"$ Combine like terms. Or factor out the common term $\"2w%2B5\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===============================================================\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"2w%5E2%2B13w%2B20\"$ factors to $\"%28w%2B4%29%282w%2B5%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In other words, $\"2w%5E2%2B13w%2B20=%28w%2B4%29%282w%2B5%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28w%2B4%29%282w%2B5%29\"$ to get $\"2w%5E2%2B13w%2B20\"$ or by graphing the original expression and the answer (the two graphs should be identical).
\n" ); document.write( " \n" ); document.write( "

\n" );